Information on Result #724700
Linear OA(2575, 631, F25, 39) (dual of [631, 556, 40]-code), using construction XX applied to C1 = C([622,35]), C2 = C([0,36]), C3 = C1 + C2 = C([0,35]), and C∩ = C1 ∩ C2 = C([622,36]) based on
- linear OA(2572, 624, F25, 38) (dual of [624, 552, 39]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,…,35}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2570, 624, F25, 37) (dual of [624, 554, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2574, 624, F25, 39) (dual of [624, 550, 40]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,…,36}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2568, 624, F25, 36) (dual of [624, 556, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(251, 5, F25, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- Reed–Solomon code RS(24,25) [i]
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(5150, 1262, F5, 39) (dual of [1262, 1112, 40]-code) | [i] | Trace Code | |
| 2 | Linear OA(2598, 697, F25, 39) (dual of [697, 599, 40]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(2599, 699, F25, 39) (dual of [699, 600, 40]-code) | [i] | ||
| 4 | Linear OA(25100, 701, F25, 39) (dual of [701, 601, 40]-code) | [i] | ||
| 5 | Linear OA(25101, 703, F25, 39) (dual of [703, 602, 40]-code) | [i] | ||
| 6 | Linear OA(25104, 757, F25, 39) (dual of [757, 653, 40]-code) | [i] | ||
| 7 | Linear OA(25105, 759, F25, 39) (dual of [759, 654, 40]-code) | [i] | ||
| 8 | Linear OA(2581, 659, F25, 39) (dual of [659, 578, 40]-code) | [i] | Varšamov–Edel Lengthening | |